Some tips

[Artaud]

This isn't a mid-game tip, but something I begin early and continue throughout the game:

Build a few small transports and give them repeat orders to take population from your home world and deposit them on select planets that you colonize.

This helps those colonies grow a bit faster. And by the time the transports return for more people, the ones they took away earlier have been replaced. So you don't have to worry about your home planet being depopulated.

I also like to rely on satellites for warp point defense.